Heights of adult men between 18 and 34 years of age are normally distributed wit

Question

Heights of adult men between 18 and 34 years of age are normally distributed with mean 69.1 inches and standard deviation 2.92 inches. One requirement for enlistment in the military is that men must stand between 60 and 80 inches tall. Find the probability that a randomly elected man meets the height requirement for military service. Twenty-three men independently contact a recruiter this week. Find the probability that all of them meet the height requirement. A regulation hockey puck must weigh between 5.5 and 6 ounces. In an alternative manufacturing process the mean weight of pucks produced is 5.75 ounce. The weights of pucks have a normal distribution whose standard deviation can be decreased by increasingly stringent (and expensive) controls on the manufacturing process. Find the maximum allowable standard deviation so that at most 0.005 of all pucks will fail to meet the weight standard.

Explanation / Answer

1)here mean =69.1

and std deviation =2.92

from normal distribution : z=(X-mean)/std deviation

.a) P(60<X<80)=P((60-69.1)/2.92<Z<(80-69.1)/2.92)=P(-3.1164<Z<3.7329)=0.9999-0.0009 =0.999

b) as probabilty of selection =0.999

hence probabilty that all of them meets the requirement =(0.999)23 =0.9770

27) for 0.005 rejection ; acceptance probability =1-0.005=0.995

hence our interval for accepted quantity should be 0.0025 to 0.9975

for 0.995 value of z from normal value table =2.807

let x is the std deviation

as mean is centered b/w specification, for meeting the criteria, upper limit =mean +x*zscore

6=5.75+x*2.807

x=0.0891

therefore std deviation should be 0.0891 ounce.

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